# Multiplicative Model Essay

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3.3. Model Specification
In order to assess the relative impact of various factors on export performance, a multiplicative model will be adopted. The model to be adopted will be in the following form;
X_t=β_0 〖R_t〗^β1 〖Y_t〗^fβ2 〖〖Ag〗_t〗^β3 〖A_t〗^β4 ε_t…………………………..1)
Where:
X_t= Quantity of horticultural exports in tonnes β_0= Constant β_1-β_4=Regression coefficients
R_t= Real exchange rate
〖Y_t〗^f= Foreign income captured by GDP per capita of major trading partners
〖Ag〗_t= Agricultural GDP over the years under study
I_t= Real interest rate ε_t= Stochastic disturbance term
For estimation purposes, model (1) can be linearized by use of the double-log as follows:
LnX=β_0+β_1 Ln〖(R〗_t)+β_2 Ln〖〖(Y〗_t〗^f)+β_3 Ln〖(Ag〗_t)+β_4 Ln(I_t )+ε_t …………………………………2)
The coefficients in the above log linear model are interpreted as elasticity (percentage change in dependent variable as a result of percentage change in the independent variable). The choice of the above variables is based purely on empirical and theoretical aspects in economics and specifically in international
The real interest rate can formally be described by the Fisher equation which defines the real interest rate as the nominal interest rate minus the inflation rate. Change in real interest rate affects exports. When the real interest rate rises, there is an increase in cost of borrowing which discourages businesses from borrowing to finance their activities. This results to a decrease in aggregate demand thereby leading to decreased productivity. In addition a high interest rate leads to more savings than investments. This is because the high interest rate increases incentive to save rather than to invest. This leads to a decrease in production hence affecting the exports. The rise in the real interest rate is mainly as a result of measures taken by the monetary policy authorities to reduce the money supply so as to reduce inflation

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